Maximin criterion

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Max-min criterion for decision making, was presented in writing on year 1950 by Abraham Wald (1902–1950). This criterion represents a pessimistic approach in decision-making (assumes the least favorable situation during taking a decision).

Application

According to the max-min criterion first for each strategy of payoff matrix, we should determine the minimum value. And then choose the strategy, for which the minimum payout, is the largest.

\(v = \underset{i}{max}\{\underset{j}{min}\{a_{ij}\}\}\)

Example

Example: we have an array of payments from the four possible decisions and three possible states:

\( \underset{Strategies}{} \diagdown \overset{States\ of\ nature} {} \) I II III
T1 200 100 120
T2 0 300 −200
T3 0 300 500
T4 −100 200 0

We are looking for a minimum winnings for each strategy, and then select the largest:

Strategies \(\underset{j}{min}\{a_{ij}\}\)
T1 100
T2 −200
T3 0
T4 −100

Summing up: According to the Max-min criterion manager should choose a strategy T1.

References